Question

From the observation deck of a skyscraper, Shaniece measures a 48^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1121 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

To find the horizontal distance from the base of the skyscraper to the ship, we can use the tangent function. Tangent of an angle is equal to the opposite side divided by the adjacent side. Substituting the values gives the horizontal distance as 1010.38 feet (rounded to the nearest hundredth).

Step-by-step explanation:

To find the horizontal distance from the base of the skyscraper to the ship, we can use the tangent function. Tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the observation deck (1121 feet) and the angle of depression is 48°.

Therefore, we have:

Tan(48°) = Opposite / Adjacent

Adjacent = Opposite / Tan(48°)

Substituting the values gives:

Adjacent = 1121 / Tan(48°)

Using a calculator, we can find that Tan(48°) is approximately 1.1106.

Hence, the horizontal distance from the base of the skyscraper to the ship is:

Adjacent = 1121 / 1.1106 ≈ 1010.38 feet (rounded to the nearest hundredth)

Answer 2

Answer: 1009.35

Step-by-step explanation: